diff options
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/round_prec.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/round_prec.c | 100 |
1 files changed, 69 insertions, 31 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/round_prec.c b/Build/source/libs/mpfr/mpfr-src/src/round_prec.c index 9dce103520f..c99d63e55ef 100644 --- a/Build/source/libs/mpfr/mpfr-src/src/round_prec.c +++ b/Build/source/libs/mpfr/mpfr-src/src/round_prec.c @@ -1,8 +1,8 @@ /* mpfr_round_raw_generic, mpfr_round_raw2, mpfr_round_raw, mpfr_prec_round, mpfr_can_round, mpfr_can_round_raw -- various rounding functions -Copyright 1999-2015 Free Software Foundation, Inc. -Contributed by the AriC and Caramel projects, INRIA. +Copyright 1999-2016 Free Software Foundation, Inc. +Contributed by the AriC and Caramba projects, INRIA. This file is part of the GNU MPFR Library. @@ -141,24 +141,40 @@ int mpfr_can_round_raw (const mp_limb_t *bp, mp_size_t bn, int neg, mpfr_exp_t err0, mpfr_rnd_t rnd1, mpfr_rnd_t rnd2, mpfr_prec_t prec) { - mpfr_prec_t err; + mpfr_prec_t err, prec0 = prec; mp_size_t k, k1, tn; int s, s1; mp_limb_t cc, cc2; mp_limb_t *tmp; MPFR_TMP_DECL(marker); + MPFR_ASSERTD(bp[bn - 1] & MPFR_LIMB_HIGHBIT); + if (MPFR_UNLIKELY(err0 < 0 || (mpfr_uexp_t) err0 <= prec)) return 0; /* can't round */ - else if (MPFR_UNLIKELY (prec > (mpfr_prec_t) bn * GMP_NUMB_BITS)) - { /* then ulp(b) < precision < error */ - return rnd2 == MPFR_RNDN && (mpfr_uexp_t) err0 - 2 >= prec; - /* can round only in rounding to the nearest and err0 >= prec + 2 */ - } MPFR_ASSERT_SIGN(neg); neg = MPFR_IS_NEG_SIGN(neg); + /* Transform RNDD and RNDU to Zero / Away */ + MPFR_ASSERTD((neg == 0) || (neg == 1)); + if (rnd1 != MPFR_RNDN) + rnd1 = MPFR_IS_LIKE_RNDZ(rnd1, neg) ? MPFR_RNDZ : MPFR_RNDA; + if (rnd2 != MPFR_RNDN) + rnd2 = MPFR_IS_LIKE_RNDZ(rnd2, neg) ? MPFR_RNDZ : MPFR_RNDA; + + if (MPFR_UNLIKELY (prec > (mpfr_prec_t) bn * GMP_NUMB_BITS)) + { /* Then prec < PREC(b): we can round: + (i) in rounding to the nearest iff err0 >= prec + 2 + (ii) in directed rounding mode iff rnd1 is compatible with rnd2 + and err0 >= prec + 1, unless b = 2^k and rnd1=rnd2=RNDA in + which case we need err0 >= prec + 2. */ + if (rnd2 == MPFR_RNDN) + return (mpfr_uexp_t) err0 - 2 >= prec; + else + return (rnd1 == rnd2) && (mpfr_uexp_t) err0 - 2 >= prec; + } + /* if the error is smaller than ulp(b), then anyway it will propagate up to ulp(b) */ err = ((mpfr_uexp_t) err0 > (mpfr_prec_t) bn * GMP_NUMB_BITS) ? @@ -168,19 +184,25 @@ mpfr_can_round_raw (const mp_limb_t *bp, mp_size_t bn, int neg, mpfr_exp_t err0, k = (err - 1) / GMP_NUMB_BITS; MPFR_UNSIGNED_MINUS_MODULO(s, err); /* the error corresponds to bit s in limb k, the most significant limb - being limb 0 */ + being limb 0; in memory, limb k is bp[bn-1-k]. */ k1 = (prec - 1) / GMP_NUMB_BITS; MPFR_UNSIGNED_MINUS_MODULO(s1, prec); - /* the last significant bit is bit s1 in limb k1 */ + /* the least significant bit is bit s1 in limb k1 */ - /* don't need to consider the k1 most significant limbs */ + /* We don't need to consider the k1 most significant limbs. + They will be considered later only to detect when subtracting + the error bound yields a change of binade. + Warning! The number with updated bn may no longer be normalized. */ k -= k1; bn -= k1; prec -= (mpfr_prec_t) k1 * GMP_NUMB_BITS; - /* if when adding or subtracting (1 << s) in bp[bn-1-k], it does not - change bp[bn-1] >> s1, then we can round */ + /* We can decide of the correct rounding if rnd2(b-eps) and rnd2(b+eps) + give the same result to the target precision 'prec', i.e., if when + adding or subtracting (1 << s) in bp[bn-1-k], it does not change the + rounding in direction 'rnd2' at ulp-position bp[bn-1] >> s1, taking also + into account the possible change of binade. */ MPFR_TMP_MARK(marker); tn = bn; k++; /* since we work with k+1 everywhere */ @@ -190,11 +212,6 @@ mpfr_can_round_raw (const mp_limb_t *bp, mp_size_t bn, int neg, mpfr_exp_t err0, MPFR_ASSERTD (k > 0); - /* Transform RNDD and RNDU to Zero / Away */ - MPFR_ASSERTD((neg == 0) || (neg ==1)); - if (MPFR_IS_RNDUTEST_OR_RNDDNOTTEST(rnd1, neg)) - rnd1 = MPFR_RNDZ; - switch (rnd1) { case MPFR_RNDZ: @@ -203,33 +220,54 @@ mpfr_can_round_raw (const mp_limb_t *bp, mp_size_t bn, int neg, mpfr_exp_t err0, /* mpfr_round_raw2 returns 1 if one should add 1 at ulp(b,prec), and 0 otherwise */ cc ^= mpfr_round_raw2 (bp, bn, neg, rnd2, prec); - /* cc is the new value of bit s1 in bp[bn-1] */ + /* cc is the new value of bit s1 in bp[bn-1] after rounding 'rnd2' */ + /* now round b + 2^(MPFR_EXP(b)-err) */ - cc2 = mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s); + mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s); + /* if there was a carry here, then necessarily bit s1 of bp[bn-1] + changed, thus we surely cannot round for directed rounding, but this + will be detected below, with cc2 != cc */ break; case MPFR_RNDN: /* Round to nearest */ - /* first round b+2^(MPFR_EXP(b)-err) */ - cc = mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s); + + /* first round b+2^(MPFR_EXP(b)-err) */ + mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s); + /* same remark as above in case a carry occurs in mpn_add_1() */ cc = (tmp[bn - 1] >> s1) & 1; /* gives 0 when cc=1 */ cc ^= mpfr_round_raw2 (tmp, bn, neg, rnd2, prec); + /* cc is the new value of bit s1 in bp[bn-1]+eps after rounding 'rnd2' */ + + subtract_eps: /* now round b-2^(MPFR_EXP(b)-err) */ cc2 = mpn_sub_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s); + /* propagate the potential borrow up to the most significant limb + (it cannot propagate further since the most significant limb is + at least MPFR_LIMB_HIGHBIT) */ + for (tn = 0; tn + 1 < k1 && (cc2 != 0); tn ++) + cc2 = bp[bn + tn] == 0; + /* We have an exponent decrease when either: + (i) k1 = 0 and tmp[bn-1] < MPFR_LIMB_HIGHBIT + (ii) k1 > 0 and cc <> 0 and bp[bn + tn] = MPFR_LIMB_HIGHBIT + (then necessarily tn = k1-1). + Then for directed rounding we cannot round, + and for rounding to nearest we cannot round when err = prec + 1. + */ + if (((k1 == 0 && tmp[bn - 1] < MPFR_LIMB_HIGHBIT) || + (k1 != 0 && cc2 != 0 && bp[bn + tn] == MPFR_LIMB_HIGHBIT)) && + (rnd2 != MPFR_RNDN || err0 == prec0 + 1)) + { + MPFR_TMP_FREE(marker); + return 0; + } break; default: /* Round away */ cc = (bp[bn - 1] >> s1) & 1; cc ^= mpfr_round_raw2 (bp, bn, neg, rnd2, prec); - /* now round b +/- 2^(MPFR_EXP(b)-err) */ - cc2 = mpn_sub_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s); - break; - } + /* cc is the new value of bit s1 in bp[bn-1]+eps after rounding 'rnd2' */ - /* if cc2 is 1, then a carry or borrow propagates to the next limb */ - if (cc2 && cc) - { - MPFR_TMP_FREE(marker); - return 0; + goto subtract_eps; } cc2 = (tmp[bn - 1] >> s1) & 1; |